7b_spatial stats-pt2

7b_spatial stats-pt2 - 12/3/2007 Lecture outline Advanced...

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12/3/2007 1 Advanced Topics in Forest Biometrics - FOR6934 Introduction to statistical models for spatial data – Part 2 Lecture outline Classical measures Distance analysis measures Nearest neighbor methods All-distance Functions Classic spatial autocorrelation statistics Moran’s I and Geary’s C These statistics compare the spatial relationship of observations in a neighborhood to the covariance relationship at pairs of locations They compare an estimate of the covariation among the Z ( s ) to an estimate of their variation These statistics are global in the sense that they estimate the overall degree of spatial autocorrelation for a dataset Also called join count statistics These statistics are applicable to lattice data Distance Analysis methods If there are patterns or clusters of data, the distribution of phenomenon may be related more to a local pattern, rather than a global pattern. Methods of Distance Analysis Nearest Neighbor K-Order Nearest Neighbor Ripley’s K Nearest Neighbor Index (NNI) Developed by Clark and Evans (1954) for describing spatial relationships in Botany data Compares the distances between nearest points and distances that would be expected under a random hypothesis (on the basis of chance) NNI is the ratio of two statistics: Nearest neighbor distance versus Expected nearest neighbor distance based on a random distribution Calculating NNI Nearest neighbor distance: where: min( d i ) is the minimum distance between the i th point and its nearest neighbor, N is the number of data points Expected nearest neighbor distance: NNI: d ( NN ) /d ( ran ) N i i N d NN d 1 ) min( ) ( N A ran d 5 . 0 ) (
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12/3/2007 2 Interpreting NNI The index is an average distance from the closest neighbor to each point with a distance that would be expected on the basis of chance If the observed average distance is the same as the mean random distance, then the ratio will be 1.0 If the observed distance is smaller than the mean
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This note was uploaded on 07/23/2011 for the course FOR 6934 taught by Professor Staff during the Spring '08 term at University of Florida.

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7b_spatial stats-pt2 - 12/3/2007 Lecture outline Advanced...

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